Learning physical properties of liquid crystals with deep convolutional neural networks

Possibilities and limitations of convolutional neural network machine learning architectures in the characterisation of achiral orthogonal smectic liquid crystals

Machine learning is becoming a valuable tool in the characterisation and property prediction of liquid crystals. It is thus worthwhile to be aware of the possibilities but also the limitations of current machine learning algorithms. In this study we investigated a phase sequence of isotropic - fluid smecticA - hexatic smectic B - soft crystal CrE - crystalline. This is a sequence of transitions between orthogonal phases, which are expected to be difficult to distinguish, because of only minute changes in order. As expected, strong first order transitions such as the liquid to liquid crystal transition and the crystallisation can be distinguished with high accuracy. It is shown that also the hexatic SmB to soft crystal CrE transition is clearly characterised, which represents the transition from short- to long-range order. Limitations of convolutional neural networks can be observed for the fluid to hexatic SmA to SmB transition, where both phases exhibit short-range ordering.

Texture identification in liquid crystal-protein droplets using evaporative drying, generalized additive modeling, and K-means Clustering

Sessile drying droplets manifest distinct morphological patterns, encompassing diverse systems, viz., DNA, proteins, blood, and protein-liquid crystal (LC) complexes. This study employs an integrated methodology that combines drying droplet, image texture analysis (features from First Order Statistics, Gray Level Co-occurrence Matrix, Gray Level Run Length Matrix, Gray Level Size Zone Matrix, and Gray Level Dependence Matrix), and statistical data analysis (Generalized Additive Modeling and K-means clustering). It provides a comprehensive qualitative and quantitative exploration by examining LC-protein droplets at varying initial phosphate buffered concentrations (0x, 0.25x, 0.5x, 0.75x, and 1x) during the drying process under optical microscopy with crossed polarizing configuration. Notably, it unveils distinct LC-protein textures across three drying stages: initial, middle, and final. The Generalized Additive Modeling (GAM) reveals that all the features significantly contribute to differentiating LC-protein droplets. Integrating the K-means clustering method with GAM analysis elucidates how textures evolve through the three drying stages compared to the entire drying process. Notably, the final drying stage stands out with well-defined, non-overlapping clusters, supporting the visual observations of unique LC textures. Furthermore, this paper contributes valuable insights, showcasing the efficacy of drying droplets as a rapid and straightforward tool for characterizing and classifying dynamic LC textures.

Genetic algorithm for the response of arbitrarily twisted nematic liquid crystals to an applied field

When an external field is applied across a liquid-crystal cell, the twist and tilt distributions cannot be calculated analytically and must be extracted numerically. In the standard approach, the Euler-Lagrange equations are derived from the minimization of the free energy of the system and then solved via finite-difference methods, often implemented in commercial software. These tools iterate from initial solutions that are compatible with the boundary conditions, providing limited to no flexibility for customization. Here we present a genetic algorithm that outputs fast and accurate solutions to the integral form of the equations. In our approach, the evolutionary routine is sequentially applied at each position within the bulk of the cell, thus overcoming the necessity of assuming trial solutions. The full range of twist angles from -90^{∘} to 90^{∘} is considered. In this way, the predictions of our routine strongly support the experimentally observed polarization transformations of light incident on different spatially varying twisted nematic liquid-crystal cells, patterned with different topologies on the two alignment layers.

Characterizing unstructured data with the nearest neighbor permutation entropy

Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has been predominantly limited to structured datasets such as time series or images. Here, we introduce the k-nearest neighbor permutation entropy, an innovative extension of the permutation entropy tailored for unstructured data, irrespective of their spatial or temporal configuration and dimensionality. Our approach builds upon nearest neighbor graphs to establish neighborhood relations and uses random walks to extract ordinal patterns and their distribution, thereby defining the k-nearest neighbor permutation entropy. This tool not only adeptly identifies variations in patterns of unstructured data but also does so with a precision that significantly surpasses conventional measures such as spatial autocorrelation. Additionally, it provides a natural approach for incorporating amplitude information and time gaps when analyzing time series or images, thus significantly enhancing its noise resilience and predictive capabilities compared to the usual permutation entropy. Our research substantially expands the applicability of ordinal methods to more general data types, opening promising research avenues for extending the permutation entropy toolkit for unstructured data.

A Siamese neural network framework for glass transition recognition

A Siamese neural network, which is a deep learning technique, was applied to investigate phase transitions based on polarising microscopic textures of liquid crystals like: antiferroelectric smectic CA* phase and its glass, smectic I phase and its glass, and smectic G and its glass. It is an example of a subtle transition without significant structural changes, where textures above and below the glass transition temperature are similar. The Siamese neural network could distinguish textures of the chosen liquid crystal phases from a glass of that phase. This publication provides details of the Siamese neural network and its implementation based on three different convolutional neural networks has been tested.

Machine learning methods for liquid crystal research: phases, textures, defects and physical properties

Liquid crystal materials, with their unique properties and diverse applications, have long captured the attention of researchers and industries alike. From liquid crystal displays and electro-optical devices to advanced sensors and emerging technologies, the study and application of liquid crystals continue to be of paramount importance in the fields of materials science, chemistry and physics. With the ever-increasing complexity and diversity of liquid crystal materials, researchers face new challenges in understanding their behaviors, properties, and potential applications. On the other hand, machine learning, a rapidly evolving interdisciplinary field at the intersection of computer science and data analysis, has already become a powerful tool for unraveling implicit correlations and predicting new properties of a wide variety of physical and chemical systems and structures. Here we aim to consider how machine learning methods are suitable for solving fundamental problems in the field of liquid crystals and what are the advantages of this artificial intelligence based approach.

Machine learning classification of polar sub-phases in liquid crystal MHPOBC

Experimental polarising microscopy texture images of the fluid smectic phases and sub-phases of the classic liquid crystal MHPOBC were classified as paraelectric (SmA*), ferroelectric (SmC*), ferrielectric (SmC1/3*), and antiferroelectric (SmCA*) using convolutional neural networks, CNNs. Two neural network architectures were tested, a sequential convolutional neural network with varying numbers of layers and a simplified inception model with varying number of inception blocks. Both models are successful in binary classifications between different phases as well as classification between all four phases. Optimised architectures for the multi-phase classification achieved accuracies of (84 ± 2)% and (93 ± 1)% for sequential convolutional and inception networks, respectively. The results of this study contribute to the understanding of how CNNs may be used in classifying liquid crystal phases. Especially the inception model is of sufficient accuracy to allow automated characterization of liquid crystal phase sequences and thus opens a path towards an additional method to determine the phases of novel liquid crystals for applications in electro-optics, photonics or sensors. The outlined procedure of supervised machine learning can be applied to practically all liquid crystal phases and materials, provided the infrastructure of training data and computational power is provided.

Using pretrained machine learning models to predict luminous and solar transmittance controllability of liquid crystal/polymer composites from microstructural images

Polarized optical microscopy (POM) images of polymer network liquid crystals (PNLCs) were first analyzed using a pretrained machine learning model for feature extraction and hierarchical clustering. The analyses worked well in predicting and improving the thermoresponsive changes individually in direct luminous and hemispheric solar transmittance, both of which are crucial properties of energy-saving smart windows. The features of a 1280 × 1920-pixel color POM image were extracted by the latest pretrained algorithm, EfficientNet-B7, as a 2560-dimensional vector and then reduced into a two-dimensional space for clustering and visualization using the uniform manifold approximation and projection (UMAP) algorithm while efficiently preserving the global structures of the distance relationship in a high-dimensional space. The feature vectors in the UMAP space were correlated with the thermoresponsive transmittance and classified using hierarchical clustering analysis. The extracted features belonging to some clusters were also correlated with the fabrication parameters. The PNLCs here were produced from various raw materials under different fabrication conditions. These analyses and predictability are extensively applied to different PNLCs for stimuli-responsive optical devices, such as solar- and privacy-control windows.

Surrogate-Assisted Hybrid-Model Estimation of Distribution Algorithm for Mixed-Variable Hyperparameters Optimization in Convolutional Neural Networks

The performance of a convolutional neural network (CNN) heavily depends on its hyperparameters. However, finding a suitable hyperparameters configuration is difficult, challenging, and computationally expensive due to three issues, which are 1) the mixed-variable problem of different types of hyperparameters; 2) the large-scale search space of finding optimal hyperparameters; and 3) the expensive computational cost for evaluating candidate hyperparameters configuration. Therefore, this article focuses on these three issues and proposes a novel estimation of distribution algorithm (EDA) for efficient hyperparameters optimization, with three major contributions in the algorithm design. First, a hybrid-model EDA is proposed to efficiently deal with the mixed-variable difficulty. The proposed algorithm uses a mixed-variable encoding scheme to encode the mixed-variable hyperparameters and adopts an adaptive hybrid-model learning (AHL) strategy to efficiently optimize the mixed-variables. Second, an orthogonal initialization (OI) strategy is proposed to efficiently deal with the challenge of large-scale search space. Third, a surrogate-assisted multi-level evaluation (SME) method is proposed to reduce the expensive computational cost. Based on the above, the proposed algorithm is named s urrogate-assisted hybrid-model EDA (SHEDA). For experimental studies, the proposed SHEDA is verified on widely used classification benchmark problems, and is compared with various state-of-the-art methods. Moreover, a case study on aortic dissection (AD) diagnosis is carried out to evaluate its performance. Experimental results show that the proposed SHEDA is very effective and efficient for hyperparameters optimization, which can find a satisfactory hyperparameters configuration for the CIFAR10, CIFAR100, and AD diagnosis with only 0.58, 0.97, and 1.18 GPU days, respectively.

Neural networks determination of material elastic constants and structures in nematic complex fluids

Supervised machine learning and artificial neural network approaches can allow for the determination of selected material parameters or structures from a measurable signal without knowing the exact mathematical relationship between them. Here, we demonstrate that material nematic elastic constants and the initial structural material configuration can be found using sequential neural networks applied to the transmmited time-dependent light intensity through the nematic liquid crystal (NLC) sample under crossed polarizers. Specifically, we simulate multiple times the relaxation of the NLC from a random (qeunched) initial state to the equilibirum for random values of elastic constants and, simultaneously, the transmittance of the sample for monochromatic polarized light. The obtained time-dependent light transmittances and the corresponding elastic constants form a training data set on which the neural network is trained, which allows for the determination of the elastic constants, as well as the initial state of the director. Finally, we demonstrate that the neural network trained on numerically generated examples can also be used to determine elastic constants from experimentally measured data, finding good agreement between experiments and neural network predictions.

Supervised Learning in Neural Networks: Feedback-Network-Free Implementation and Biological Plausibility

The well-known backpropagation learning algorithm is probably the most popular learning algorithm in artificial neural networks. It has been widely used in various applications of deep learning. The backpropagation algorithm requires a separate feedback network to back propagate errors. This feedback network must have the same topology and connection strengths (weights) as the feed-forward network. In this article, we propose a new learning algorithm that is mathematically equivalent to the backpropagation algorithm but does not require a feedback network. The elimination of the feedback network makes the implementation of the new algorithm much simpler. The elimination of the feedback network also significantly increases biological plausibility for biological neural networks to learn using the new algorithm by means of some retrograde regulatory mechanisms that may exist in neurons. This new algorithm also eliminates the need for two-phase adaptation (feed-forward phase and feedback phase). Hence, neurons can adapt asynchronously and concurrently in a way analogous to that of biological neurons.

Machine Learning of Implicit Combinatorial Rules in Mechanical Metamaterials

Combinatorial problems arising in puzzles, origami, and (meta)material design have rare sets of solutions, which define complex and sharply delineated boundaries in configuration space. These boundaries are difficult to capture with conventional statistical and numerical methods. Here we show that convolutional neural networks can learn to recognize these boundaries for combinatorial mechanical metamaterials, down to finest detail, despite using heavily undersampled training sets, and can successfully generalize. This suggests that the network infers the underlying combinatorial rules from the sparse training set, opening up new possibilities for complex design of (meta)materials.

Gradient dynamics in reinforcement learning

Despite the success achieved by the analysis of supervised learning algorithms in the framework of statistical mechanics, reinforcement learning has remained largely untouched by physicists. Here we move towards closing the gap by analyzing the dynamics of the policy gradient algorithm. For a convex problem, namely the k-armed bandit, we show that the learning dynamics obeys a drift-diffusion motion described by a Langevin equation, the coefficients of which can be tuned by the learning rate. We explore the striking similarity between our Langevin equation and the Kimura equation, describing genotypes evolution. Furthermore, we propose a mapping between a nonconvex reinforcement learning setting describing multiple joints of a robotic arm and a disordered system, namely a p-spin glass. This mapping enables us to show how the learning rate acts as an effective temperature and thus is capable of smoothing rough landscapes, corroborating what is displayed by the drift-diffusive description and paving the way for physics-inspired algorithmic optimization based on annealing procedures in disordered systems.

Determining usefulness of machine learning in materials discovery using simulated research landscapes

When existing experimental data are combined with machine learning (ML) to predict the performance of new materials, the data acquisition bias determines ML usefulness and the prediction accuracy. In this context, the following two conditions are highly common: (i) constructing new unbiased data sets is too expensive and the global knowledge effectively does not change by performing a limited number of novel measurements; (ii) the performance of the material depends on a limited number of physical parameters, much smaller than the range of variables that can be changed, albeit such parameters are unknown or not measurable. To determine the usefulness of ML under these conditions, we introduce the concept of simulated research landscapes, which describe how datasets of arbitrary complexity evolve over time. Simulated research landscapes allow us to use different discovery strategies to compare standard materials exploration with ML-guided explorations, i.e. we can measure quantitatively the benefit of using a specific ML model. We show that there is a window of opportunity to obtain a significant benefit from ML-guided strategies. The adoption of ML can take place too soon (not enough information to find patterns) or too late (dense datasets only allow for negligible ML benefit), and the adoption of ML can even slow down the discovery process in some cases. We offer a qualitative guide on when ML can accelerate the discovery of new best-performing materials in a field under specific conditions. The answer in each case depends on factors like data dimensionality, corrugation and data collection strategy. We consider how these factors may affect the ML prediction capabilities and discuss some general trends.

Inference of molecular orientation/ordering change nearby topological defects by the neural network function from the microscopic color information

Topological defects in liquid crystals (LCs) dominate molecular alignment/motion in many cases. Here, the neural network (NN) function has been introduced to predict the LC orientation condition (orientation angle and order parameter) at local positions around topological defects from the phase/polarization microscopic color images. The NN function was trained in advance by using the color information of an LC in a planar alignment cell for different orientation angles and temperatures. The photo-induced changes of LC molecules around topological defects observed by the time-resolved measurement was converted into the image sequences of the orientation angle and the order parameter change. We found that each pair of brushes with different colors around topological defects showed different orientation angle and ordering changes. The photo-induced change was triggered by the photoisomerization reaction of molecules, and one pair of brushes increased in its order parameter just after light irradiation, causing gradual rotation in the brush. The molecules in the other pair of brushes were disordered and rotated by the effect of the initially affected region. This combination approach of the time-resolved phase/polarization microscopy and the NN function can provide detailed information on the molecular alignment dynamics around the topological defects.

Characterising soft matter using machine learning

Machine learning is making a major impact in materials research. I review current progress across a selection of areas of ubiquitous soft matter. When applied to particle tracking, machine learning using convolution neural networks is providing impressive performance but there remain some significant problems to solve. Characterising ordered arrangements of particles is a huge challenge and machine learning has been deployed to create the description, perform the classification and tease out an interpretation using a wide array of techniques often with good success. In glass research, machine learning has proved decisive in quantifying very subtle correlations between the local structure around a site and the susceptibility towards a rearrangement event at that site. There are also beginning to be some impressive attempts to deploy machine learning in the design of composite soft materials. The discovery aspect of this new materials design meets the current interest in teaching algorithms to learn to extrapolate beyond the training data.